Nonparametric Bayes Tutorial

This tutorial took place in January 2017 at MIT Lincoln Labs, USA. See this link for the latest versions and videos of this tutorial.

Part I: Monday, January 9, 10:00–11:30AM
Part II: Friday, January 13, 1:00–2:30 PM
Part III: Friday, January 13, 3:00–4:30 PM

Instructor:
Professor Tamara Broderick
Email:

Description

Nonparametric Bayesian methods make use of infinite-dimensional mathematical structures to allow the practitioner to learn more from their data as the size of their data set grows. What does that mean, and how does it work in practice? In this tutorial, we'll cover why machine learning and statistics need more than just parametric Bayesian inference. We'll introduce such foundational nonparametric Bayesian models as the Dirichlet process and Chinese restaurant process and touch on the wide variety of models available in nonparametric Bayes. Along the way, we'll see what exactly nonparametric Bayesian methods are and what they accomplish.

Materials

README for demos
Slides for Part I
- Demo 1 [code]: Beta random variable and random distribution intuition
- Demo 2 [code]: Dirichlet random variable and random distribution intuition
- Demo 3 [code]: K large relative to N intuition; empty components
- Demo 4 [code]: K large relative to N intuition; growth of number of clusters
- Demo 5 [code]: GEM random distribution intuition
Slides for Part II
- Demo 6 [code]: An exact DPMM simulator
Slides for Part III
- Demo 7 [code]: A CRP mixture model sampler

Prerequisites

Know what a prior, likelihood, and posterior are.
Know how to use Bayes' Theorem to calculate a posterior for both discrete and continuous parametric distributions.
Understand what a generative model is.
Have a basic idea of what Gibbs sampling is and when it is useful (at least check out the Wikipedia article in advance).

What we won't cover

Gaussian processes are an important branch of nonparametric Bayesian modeling, but we won't have time to cover them here. We'll be focusing on the discrete, or Poisson point process, side of nonparametric Bayesian inference.